Problem: Simplify the following expression: $y = \dfrac{1}{10x} + \dfrac{1}{8x}$
Solution: In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $10x$ and $8x$ $\lcm(10x, 8x) = 40x$ $ y = \dfrac{4}{4} \cdot \dfrac{1}{10x} + \dfrac{5}{5} \cdot \dfrac{1}{8x} $ $y = \dfrac{4}{40x} + \dfrac{5}{40x}$ $y = \dfrac{4 +5}{40x}$ $y = \dfrac{9}{40x}$